Problem: Simplify the following expression: $z = \dfrac{a^2 - 16a + 63}{a - 7} $
First factor the polynomial in the numerator. $ a^2 - 16a + 63 = (a - 7)(a - 9) $ So we can rewrite the expression as: $z = \dfrac{(a - 7)(a - 9)}{a - 7} $ We can divide the numerator and denominator by $(a - 7)$ on condition that $a \neq 7$ Therefore $z = a - 9; a \neq 7$